For the dressing: in a medium mixing bowl, add the olive oil, lemon juice/vinegar and use a fork or hand whisk to mix well. Add the garlic, mustard, parmesan, mayonnaise and anchovy. Season with salt & pepper and mix to creamy dressing. Set aside.
Heat the oil in a large wide pan and fry the mushrooms until cooked & golden. Season with salt & pepper and set aside.
In a large non-stick pan, fry the bacon until crispy, then drain on kitchen paper. Cut into fine strips.
Boil the eggs for 7 minutes in water, then transfer to a bowl of cold water to cool. Peel and slice in half, then set aside.
To assemble: Toss the lettuce with half the dressing, then arrange the leaves on a platter. Top with the mushrooms, bacon, eggs and croutons. Top with more parmesan cheese and serve at once.